Unlike as in the case of single sequences there are double sequences which are convergent in Pringsheim's sense but unbounded. That is, the set \(\mathcal {C}_p\setminus \mathcal {M}_u\)  is not empty. Boos [1]} defined the sequence \(x=(x_{mn})\)  by
\(x_{mn}=\left\lbrace \begin{array}{ccl}n&, & m=0, n\in \mathbb {N} \\0&, & m\ge 1, n\in \mathbb {N},\end{array}\right.\) 
